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Full text of "Mathematical And Physical Papers - Iii"

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Baily's results with a long brass tube and with long cylindrical rods.
				Add for	Total tt	n	
No.	2 a.	nx	k	confined	by	by expe-	Difference.
			\  space.		theory.	riment.	
35 to 38	1-5	5'849	1-242	0-122	2-364	2-290	 0*074, or  ^j-
21 or 42	0-410	1-555	1-917	0-009	2-926	2-932	+ 0-006, or + -&Q
43	0-185	0-7089	3-055     0*002		4-057	4-083	4-0-026, or +rh
44	0-072	0-2759	6-670		7-670	7-530	-0-140, or -T&
It will be seen at once how closely the experiments are represented by theory. The largest proportionate difference occurs in the case of the brass tube, and even that is less than one-thirtieth. A glance at Baily's wood-cut at page 417 will shew that the six planes with which the tube was furnished caused the whole figure to deviate sensibly from the cylindrical form. Moreover the resistance experienced by each element of the cylinder has been calculated by supposing the element in question to belong to an infinite cylinder oscillating with the same linear velocity, and the resistance thus determined must be a little too great in the immediate neighbourhood of the ends of the cylinder, where the free motion of the air is less impeded than it would be if the cylinder were prolonged. Lastly, the correction for confined space is calculated according to the ordinary equations of hydrodynamics, and on that account, as well as on account of the abrupt termination of the cylinder, will be only approximate. The small discrepancy between theory and observation, as well as the small difference (amounting to about the l-83rd of the whole) detected by experiment between the results obtained with the extreme planes and those obtained with the mean planes, may reasonably be attributed to some such causes as those just mentioned. In the case of the steel rod or wire, the difference between theory arid observation may be altogether removed by supposing a very small error to have existed in the measurement of the diameter of the rod. Since, as we have seen, the observation is satisfied by m ='02822, and (147) gives aoctlt when pf and r are constant, it is sufficient, in order to satisfy the experiment, to increase the diameter of the rod in the ratio of 0'2759 to 02822, or to suppose an error of